A Garden of Eden pattern, discovered by R. Banks in 1971, the first such pattern discovered in Conway's Game of Life.

The smallest known Garden of Eden pattern for Life, as of 2005.

In the study of cellular automata, Garden of Eden patterns are configurations that cannot be reached from any other starting configuration. They are named after the biblical Garden of Eden because they have no predecessor configurations—they must be created as such. Garden of Eden pattern (ugly), made by myself File links The following pages link to this file: Garden of Eden pattern User:Kieff/Gallery Categories: BSD images ... Garden of Eden pattern (ugly), made by myself File links The following pages link to this file: Garden of Eden pattern User:Kieff/Gallery Categories: BSD images ... Gosper Glider Gun creating gliders. The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. ... Image File history File links The smallest known Garden of Eden pattern known for Conways Game of Life (as of 2005). ... Image File history File links The smallest known Garden of Eden pattern known for Conways Game of Life (as of 2005). ... A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... The Fall of Man by Lucas Cranach, a 16th century German depiction of Eden Garden of Eden, from Hebrew Gan Eden, גן עדן is the location of the story told in Genesis 2 and 3—part of the creation belief of the Abrahamic religions. ...

These configurations were named by John Tukey in the 1950s, long before John Conway invented his Game of Life. John Wilder Tukey (June 16, 1915 - July 26, 2000) was a statistician. ... John Horton Conway (born December 26, 1937, Liverpool, England) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. ... Gosper Glider Gun creating gliders. The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. ...

General consequences

Let some configuration at timestep t be denoted by C_t, and the function (the automaton) f to map the configuration C_t to C_t+1.

A Garden of Eden pattern G_t means that there does not exist any configuration G_t-1 such that f(G_t-1)=G_t. This means a cellular automaton which possesses Garden of Eden pattern(s) is not surjective. In mathematics, a surjective function (or onto function or surjection) is a function with the property that all possible output values of the function are generated when the input ranges over all the values in the domain. ...

One other characteristic of certain cellular automata is that of "reversibility", that is, given a configuration C_t, there is a unique predecessor configuration C_t-1 easily determined from C_t. This condition implies that the automaton function is bijective. From the definition of bijectivity, cellular automata which possess Garden of Eden patterns are clearly not reversible. In fact, all non-injective automata possess Garden of Eden patterns. Since the Game of Life is easily seen not to be injective, it was known such patterns existed in it even before any were discovered. In mathematics, a bijection, bijective function, or one-to-one correspondence is a function that is both injective (one-to-one) and surjective (onto), and therefore bijections are also called one-to-one and onto. ... In mathematics, an injective function (or one-to-one function or injection) is a function which maps distinct input values to distinct output values. ...

Garden of Eden patterns are not unique.

External links

• Garden of Eden (Eric Weisstein's Treasure Trove of The Game of Life)